It's all Greek
This project examines:
* How Greek patterns can help in studying shape, number and early algebra.
* How maths can be used when going on holiday.
It also investigates mathematical legacies, intricate geometric designs and the lure of the Aegean sun - truly something for everyone about to take a summer holiday.
SCHOOL IN ANCIENT GREECE
If you had gone to school in ancient Greece you might have done calculations using an abacus like the one above. The bad news is that only boys went to school! Famous buildings, such as the Parthenon, show that the ancient Greeks had a strong understanding of geometry and proportion.
Many Greek words and symbols are still used in maths today. For example, triangles with two sides the same are called isosceles, a Greek word meaning "equal legs".
Many important mathematical ideas are associated with the ancient Greeks. Eratosthenes was known for his method of finding prime numbers. Other famous Greek mathematicians include Pythagoras and Euclid.
The following method - which is often used for finding prime numbers under a hundred - is based on the method used by Eratosthenes.
* Using a hundred-square grid (numbered 1-10 on the top line, 11-20 on the second line, and so on, with 91-100 on the last line) start with your pencil on number 2 - but don't cross it out.
* Count on 2 and cross out the number you land on (4). Continue in this way crossing out multiples of 2 up to 100.
* Repeat, starting on 3 and crossing off every third number after it (leave 3 but cross out 6,9,12... You could do this in a different colour to the one used for multiples of 2).
* Repeat starting on 4... Then 5... Then 6. Continue until multiples of 10 have been crossed out.
The numbers from 2 onwards that are not crossed out are all prime.
* Can you see any patterns in the multiples of different numbers?
* Why is it unnecessary to list multiples of numbers above 10 to find primes up to a hundred?
The ancient Greeks knew that an isoscelestriangle (one with two equal sides) also has two equal angles.
* Can you draw an isosceles triangle with a right angle?
* Can you draw an isosceles triangle in which one side is twice as long as one of the other sides?
* Do isosceles triangles have line symmetry? How about rotational symmetry?
MATHS AS DECORATION
Ancient Greeks made wide use of geometric patterns, especially as borders around plates or vases. Investigate different border patterns to see how the patterns are repeated and whether you can find lines of symmetry.
* Design a border pattern of your own on squared or dotted paper. Which type of symmetry is present?
* Investigate different ways of drawing spirals on squared or dotted paper. Can you say which type of symmetry is present?
* Programme a floor robot (such as PIP or Roamer)to move in a spiral, or draw spirals using a computer language such as Logo.
* Find border patterns containing two-coloured squares. Investigate different ways of colouring the squares.
The patterns below have different types of symmetry because they are repeated in different ways.
The top pattern has vertical lines of symmetry. You can check this by placing a mirror vertically on the pattern.
The second design is repeated by translation, which means the pattern is moved along sideways. To check this, trace over part of the pattern then move the tracing paper along till it matches again.
The third pattern is repeated by translation but also has a horizontal line of symmetry.
Some border patterns contain squares coloured part black and partly orange.
* For each square shown, what fraction is coloured black? What fraction is coloured orange?
* Draw squares 4cm by 4cm and investigate different ways of colouring each square half black and half orange.
Draw a spiral on squared paper using linesof length 1,1,2,2,3,3cm and turning through 90 degrees after each line.
* What is the total length of the spiral?
* Add lines of 4cm and 4cm. How long is the spiral now?
* Continue adding the next two lines and calculating the total. Can you spot a pattern?
* How long will your spiral be when the last two lines are 10cm and 10cm?
Postcards and photos give clues about what modern Greece is like, but graphs, charts and figures also give you information.
Holiday brochures often give graphs so you can compare the weather abroad with that here.
Look in newspapers to find out how much foreign currency to expect for every pound you plan to take with you.
Holiday brochures tell you when your flight leaves and how long it takes. You can work out the arrival time on your watch, but it may differ from local time.
These are found in phone books. Use them to change your arrival time to local time.
WEATHER IN GREECE
* What is the temperature in Athens in:
a) February b) July c) November?
* How much hotter is Athens than London in:
a) January b) August c) November?
* Based on these temperatures, what clothing might you pack for a holiday in Greece?
EXCHANGE RATES IN GREECE
Suppose a bank is offering Greek currency at an exchange rate of 480 drachma to the pound.
* How many drachma (dr) will you get in exchange for: a) Pounds 10 b) Pounds 5 c) Pounds 100 d) Pounds 50?
Suppose you buy the following items in Greece
* a) an ice cream for 240 dr b) sunglasses for 960dr. What are these prices equal to in pounds or pence?
If you take one of the following flights, what will be the time on your watch when the flight arrives?
* Gatwick to Corfu departs 6:15, flight time 3 hours.
* Manchester to Crete departs 7:00, flight time 4.25 hours.
* Glasgow to Rhodes departs 19:55, flight time 4.5 hours.
This is an opportunity to use mathematical language, such as "multiple" and "prime", as well as a chance to look at patterns of multiples or to apply tests for divisibility. Children could also be asked which multiples they need to exclude before listing all the primes up to 400 or other numbers. (For 400, stop at 20 because 400 = 202, so pairs of factors must be one bigger and one smaller than this).
The two-colour activities give the opportunity to discuss pairs of fractions that total 1 and simple equivalent fractions. The number of answers in the halving investigation often surprises children, especially when they start using lines other than those on the squared paper, such as curved lines.
When the spiral has a width of 3cm, the total length is 12 (3 x 4cm), for which 4 length is 20 (4 x 5cm). In general the length is n (n + 1cm) where n is the length (in cm) of the last two lines, so finishing at 10cm gives a length of 110cm.
Weather in Greece
You may wish to discuss what average daily maximum means or to calculate it over a month using a maxmin thermometer. Many holiday brochures give temperatures in degrees fahrenheit so you could convert them, perhaps using a conversion graph.
Using rates for other countries (such as 9.4 francs to a pound) can lead to multiplying decimals by 10, 100 and so on. Changing drachma to